Back when that photo was taken, Perth was just like any other major town at the time which was the primary urban centre for a 20 mile radius with it's joint services. It still is, though smaller towns and villages the likes of Murthly, Luncarty, Crieff, Bankfoot, Almnondbank, Blairgowrie, Pitcairngreen, Coupar Angus, and Stanley, had much higher demand for Perth specifically. Death of the high street, Dr Beeching, the M90, and such like over the years has reduced the need for Perth to be the epicentre it once was - and the city is now all but desolate until the council get their act together.
Apart from the usual errands, most of the travel demand in and around Perth is for Dundee mostly, as well as the central belt, with it having probably the highest proportion of Dundee bound journeys of any city outside Edinburgh and Glasgow (around 1 in 5 by rail alone). These communities are expanding rapidly; particularly Bridge of Earn, Newburgh, Murthly, Luncarty, and Almondbank - and there's a major community building project happening which will eventually link up Almondbank with Perth itself, as well as the much needed vital missing link over the Tay to hook Scone, Blairgowrie, and Coupar Angus directly with the A9 to alleviate the need to traverse Perth. Add that to the economic growth of the A9 duelling and Perth is got an underestimated handful to cope with, particularly in the north west of the city and towards the south east.
For any service to maximise it's potential, there would need to be infrastructure improvements between Newburgh and Dunkeld - mainly duelling and line side clearence. Over the past year or two a number of construction projects have happened within close vacinity of the HML north of Perth in the Inveralmond and Luncarty area, with more set to happen in and around Stanley. If key areas adjacent to the line were to be safeguarded , I see no reason at all why a local service wouldn't have the demand to operate within the next decade or so. I wouldn't go as far to say that Blair Atholl would merrit this though. Pitlochry at a push, but running to Dunkeld would be at least a start. But we're talking later rather than sooner.
In sooner terms, Perth is at breaking point in terms of traffic. I don't know if there's a term for it but it's become an interchange city for somewhere else. The city itself is starting to crumble in terms of it's transport infrastructure, as anyone who is familiar with the current bomb site of a bus station. But the demand for better transport links from these communities within a 10 mile radius is sky high. Once the Bertha Park scheme is finished, it'll go beyond what Perth can handle. Indeed it is starting to show now.
To hazard an 'at most' scenario, by 2030/40 I can see the current Edinburgh local being extended to Dunkeld and serving up to 8 new stations. If that Scottish Green proposed pop up station scheme is ever going to come to fruition, then I can such areas around Perth beneffiting most. Right now though, I can only see up to 5 areas in the region that would merrit any sort of look in at a rail station - 2 of them are the only one's for definite which unquestionably need them now.